Chapter 5

Production

The preceding two chapters discussed consumption;
this chapter discusses production. For simplicity we assume that
there is only a single input to production, the producer's time,
which may be used to produce any one of a variety of goods. You may
think of these goods either as services, such as lawn mowing or dish
washing, or as objects produced from raw materials that are freely
available. Alternatively, you may want to think of the producer as
actually an employee who produces some form of labor (assembling
automobiles, painting houses) and sells it to a firm that combines
labor with other inputs to produce goods.

Implicit in the assumption of a single input and a
single output is the further assumption that the producer is
indifferent between an hour spent mowing lawns and an hour spent
washing dishes. Otherwise there would have to be either an additional
input (unpleasantness of mowing lawns) or an additional (perhaps
disvalued) output (getting grass all over my clothes), which would
violate our assumption of only one input and one output.

In Chapter 9, we will analyze more complicated
forms of production. Each production unit (a firm rather than a
single worker) will have a production
function, showing how it can combine
inputs, such as labor and raw materials, to produce different
quantities of output. The production decision will then involve
several steps. The firm must first find, for any quantity of output,
the lowest cost way (combination of inputs) to produce it; once it
has done so, it will know the cost of producing any quantity (its
total cost function). Given that information and the market price,
the firm decides how much to produce in order to maximize its
profit.

PART I -- THE ARGUMENT

In Chapters 3 and 4, we derived the demand curve
for a good from the preferences of the consumer; in this chapter, we
will be deriving supply curves from the preferences and abilities of
the producers. The first step is to see how a potential producer
decides which good to produce. The next is to see how he decides how
many hours to work. The final step is to consider the situation in
which there are many different producers, so that the supply curve is
the sum of their individual supply curves.

Choosing a Good to Produce

Table 5-1 shows the output per hour, the price,
and the implicit wage for each of three goods--mowed lawns, washed
dishes, and meals. The price for a mowed lawn is $10 and the producer
can mow 1 lawn per hour, so the implicit wage is $10/hour. Similarly,
washing 70 dishes per hour at $0.10/dish yields a wage of $7/hour,
and cooking 2 meals per hour at $3/meal yields $6/hour. Since the
only difference among the alternatives (from the standpoint of the
producer) is the implicit wage, he chooses to mow lawns. Note that
this decision depends on (among other things) the price. If the price
for mowing a lawn were less than $7 (and the other prices were as
shown in the table), he would wash dishes instead.

Table 5-1

Lawn Mowing

Dish Washing

Cooking

Output

1 lawn/hour

70 dishes/hour

2 meals/hour

Price

$10/lawn

$.10/dish

$3/meal

Wage

$10/hour

$7/hour

$6/hour

The Supply of Labor

Figure 5-1a shows a graph of the marginal
disvalue of
labor as a function of the number of hours worked. If you were
enjoying 24 hours per day of leisure (doing no work at all), it would
take only a small payment ($0.50 in the figure) to make you willing
to work for a single hour; you would be indifferent between zero
hours a day of work and 1 hour of work plus $0.50. If, on the other
hand, you were already working 10 hours a day, it would take a little
over $10 to make you willing to work an additional hour.

Suppose the wage is $10/hour and you are working 5
hours per day. You would be willing to work an additional hour for an
additional payment of about $3; since you can actually get $10 for
it, you are obviously better off working the extra hour. The same
argument applies as long as the marginal disvalue of labor to you is
less than the wage, so you end up working that number of hours for
which the two are equal. The number of hours of labor you supply at a
wage of $10 is the number at which your marginal disvalue for labor
is equal to $10. The same relation applies at any other wage, so your
marginal disvalue for labor curve is also your supply curve for labor, just as,
in Chapter 4, your marginal value curve for a good was also your
demand curve.

Presumably leisure, like other goods, is worth
less to you the more of it you have--it has declining marginal value.
The cost to you of an hour of labor is giving up an hour of
leisure--the less leisure you have, the greater that cost. So if
leisure has decreasing marginal value, labor has increasing marginal
disvalue. That fits my experience, and probably yours; the more hours
a day I am working, the less willing I am to work an additional hour.
Since the marginal disvalue of labor curve is increasing, the supply
curve, showing how many hours you choose to work as a function of the
wage you receive, is upward sloping as well. The more you are paid
for each hour of labor, the more hours you choose to work.

Producer Surplus

We can now define producer surplus in a way
analogous to consumer surplus. Suppose the wage is $10/hour. You are
willing to work the first hour for $0.50; since you actually receive
$10 for it, your net gain is $9.50. The next hour is worth about a
dollar to you; you receive $10 for a gain of $9. Summing these gains
over all the hours you work gives us the colored area of Figure
5-1a.

Note that the benefit to you of being able to work
for $10/hour--your producer
surplus--is not the same as the salary you
get. Working 10 hours at a wage of $10/hour gives you a salary of
$100/day. This is not, however, your gain from working. To find that,
you must subtract out the cost to you of working--the value to you of
the time that you spend working instead of doing something else. Your
salary is the area of a rectangle ten hours/day wide by ten
dollars/hour high--the sum of the shaded and the colored regions on
Figure 5-1a. The value to you of your time--the total disvalue to you
of working 10 hours a day--is the shaded area under the supply curve;
you might think of it as how much worse off you would be if you were
forced to work 10 hours per day and paid nothing. The rectangle minus
the area under the supply curve is the area above the supply
curve--your producer surplus, the amount by which you are better off
working at $10/hour than not working at all.

The result, as you can see, is very much like the
result for consumer surplus in the previous chapter. The consumer
buys goods; their total value to him is measured by the area under
his marginal value curve. He pays for them an amount equal to the
rectangle price times quantity. His consumer surplus is the
difference between the value of what he gets and what he pays--the
area under the marginal value curve and above the price. The producer
sells his leisure; its value to him is measured by the area under his
marginal value for leisure curve, which is the same as his marginal
disvalue for labor curve. He receives in exchange the rectangle wage
times number of hours worked--the price for selling his leisure
(working) times the amount of leisure sold (number of hours worked).
His producer surplus is the difference between what he gets for his
work and what it cost him--the value of the leisure he gives
up--which is the area below the wage and above the marginal disvalue
of labor curve. The marginal disvalue for labor curve is the supply
curve for labor just as the marginal value for apples curve is the
demand curve for apples.

Producer surplus, the marginal disvalue for
labor, and the supply curve for lawn mowing. The area above the marginal disvalue for labor curve and
below $10/hour is the producer surplus from being able to work at
$10/hour. The colored area above the supply curve for lawns and below
the price is the producer surplus from mowing lawns at that price
($10/lawn). The supply curve is horizontal at the price at which you
are indifferent between lawn mosing and your next most profitable
production opportunity (dish washing).

The Supply of Goods--One Producer

We now have the supply curve for labor, but what
we want is the supply curve for mowed lawns. Since I can mow 1 lawn
per hour, a price of $10/lawn corresponds to a wage of $10/hour and a
labor supply of 10 hours per day corresponds to mowing that many
lawns. It appears that the supply curve for lawns and for labor are
the same; all I have to do is relabel the vertical axis "price in
$/lawn" and the horizontal axis "lawns/day."

Appearances are deceiving; the supply curve for
lawns is not the same as for labor. My decision to mow lawns instead
of spending my time producing something else depended on the price I
could get for doing so. If that price drops below $7/lawn, my output
of mowed lawns drops to zero; I am better off washing dishes instead.
The resulting supply curve is shown on Figure 5-1b. The colored area
is my producer surplus from producing mowed lawns at $10/lawn. To see
why my producer surplus does not include the shaded area below the
line at $7/lawn, consider what my producer surplus would be if I
could get $7 for each lawn I mowed. How much better off am I being
able to mow lawns at $7 than not mowing lawns? I am not better off at
all; at that wage, I can do just as well washing dishes.

This is another example of the idea of opportunity
cost, discussed in Chapter 3. The cost to me of mowing lawns is
whatever I must give up in order to do so. If the best alternative
use of my time is leisure, as it is for the solid part of curve S on
Figure 5-1b, then the cost is the value of my leisure. If the best
alternative use is washing dishes, as it is on the dashed part of S,
then the cost is the money I would have gotten by washing
dishes.

Going from the supply curve for labor to the
supply curve for mowed lawns was particularly simple because the rate
at which I mow is 1 lawn per hour. Suppose the grass stops growing,
someone invents an automatic dishwasher, and I become a cook. Figure
5-2 shows my supply curve for meals, given that my supply curve for
labor is as shown on Figure 5-1a.

To derive Figure 5-2, we note that each hour of
work produces 2 meals (Table 5-1). Hence I earn $10/hour cooking if
the price for meals is $5/meal. Working 10 hours/day, which is what I
do if I get $10/hour, produces 20 meals/day. So point B on Figure
5-1a ($10/hour and 10 hours/day) corresponds to point b on Figure 5-2
($5/meal and 20 meals/day); similarly point A corresponds to point a.
The supply curve for meals is the same as the supply curve for labor
except that it is "squished" vertically (by a factor of 2) and
"stretched" horizontally (by a factor of 2). Unlike the supply curve
for mowed lawns shown on Figure 5-1b, it has no horizontal
segment--because, by assumption, meals are the only thing left to
produce.

The supply curve for cooking
meals. This supply curve is the same as
the supply curve for labor, except that each hour worked corresponds
to two meals cooked and each dolar per meal corresponds to $2/hour.
Points a and b correspond to points A and B on Figure 5-1a.

More Than One Producer

So far, I have considered the supply curve of a
single producer. If we have more than one, there is no reason to
assume they will all be equally good at producing the different
goods, nor that they will all have the same supply curves for labor.
If they do not, then their supply curves for mowed lawns--or other
goods--will also be different, with the horizontal sections occurring
at different prices according to their relative skills at different
kinds of production. A producer who is very good at mowing lawns
(many mowed per hour) or very bad at doing anything else will choose
to mow lawns even if the price is low. A producer who is bad at
mowing lawns (many hours per lawn) or good at something else will mow
lawns only when the price is high. Figure 5-3 shows the supply curves
for two such producers, A(nne) and B(ill), and their combined supply
curve.

At prices below $2.50/lawn, neither Anne nor Bill
produces. At prices above $2.50/lawn but below $5/lawn, only Anne
produces; the combined supply curve is the same as her supply curve.
At a price of $5, Bill abruptly enters the market, mowing 6 lawns per
day; adding that to Anne's output of 9 gives a total output of 15.
When the price goes from $5 to $6, Anne increases her output by
another unit and so does Bill; so total output goes up by 2 to
17.

The combined supply curve is a horizontal sum. The summation is
horizontal because we are summing quantities (shown on the
horizontal axis) at each price. Both A and B can sell their products
at the same price; whatever that price is, total quantity supplied is
the (horizontal) sum of what they each produce. The same would be
true if we were deriving a total demand curve from two or more
individual demand curves. All consumers in a market face the same
price, so total quantity demanded at a price is the quantity consumer
A demands plus the quantity consumer B demands plus . . . .

The sum of the producer surplus that B receives at
a price of $6 plus the producer surplus that A receives is equal to
the producer surplus calculated from the combined supply curve--the
area above their combined supply curve and below the horizontal line
at $6. The reason is shown on Figures 5-3a through 5-3c. Consider the
narrow horizontal rectangle R shown in Figure 5-3a. Its height is
[[Delta]] P, its width is QA+B = qA +qB ; so its area is [[Delta]] P
x (QA+B ) =
([[Delta]] P x qA) + ([[Delta]] P x qB) = RA + RB on Figures 5-3b and 5-3c.
The same applies to all of the other little horizontal rectangles
that make up the producer surplus; in each case, the area of the
rectangle on Figure 5-3a, showing the summed supply curve, is the sum
of the areas of the rectangles on Figures 5-3b and 5-3c, which show
the individual supply curves. So the shaded area on Figure 5-3a
equals the sum of the shaded areas on 5-3b and 5-3c. The shaded areas
are not precisely equal to the corresponding surpluses, since the
rectangles slightly overlap the supply curve; but the thinner the
rectangles are, the smaller the discrepancy. In the limit as the
height of the rectangles ([[Delta]] P) goes to 0, the shaded areas
become exactly equal to the corresponding producer surpluses; so the
producer surplus calculated from the summed supply curve is the sum
of the producer surpluses from the individual supply curves.

The result applies to any number of producers, as
does a similar result for the consumer surplus of any number of
consumers. So we can find the sum of the surpluses received by
consumers or producers by calculating the surplus for their combined
demand or supply curve just as if it were the demand or supply curve
for a single individual. This fact will be important in Chapter 7,
where we analyze the cost that taxes impose on producers and
consumers, and elsewhere.

Figure 5-3

The producer surplus for a two producer supply
curve. The colored rectangle R is the sum
of RA and
RB, and
similarly for the other rectangles. So the shaded area on Figure 5-3a
is the sum of the shaded areas on Figures 5-3b and 5-3c. AsP approaches zero, the shaded area
on each figure becomes exactly (instead of approximately) equal to
the corresponding producer surplus. Hence the producer surplus
calculated from the summed supply curve SA+B is the sum of the producer
surplus calculated from SA and SB.

We now have two different reasons to expect that
supply curves will slope up. The first is the increasing marginal
disvalue of labor. The second is that as the price of a good rises,
more and more people find that they are better off producing that
good than producing anything else. As each new producer comes in, the
supply curve gets a new horizontal segment--the increased price
results in increased quantity above and beyond any increased
production by existing producers. This will prove important in the
next section, where we see that the first reason for expecting supply
curves to slope up is less powerful than it at first appears.

PART 2 -- SOME PROBLEMS

Look again at Figure 5-1a, and think about what it
means. At a wage of $1/hour, the producer is working 2 hours per day
and earning $2/day. It may be possible to live on an income of
$730/year, but it is not easy. At a wage of $15/hour, the same
individual chooses to work 12 hours per day and earn $65,700/year.
There are probably people earning that kind of money who work those
hours for 365 days per year, but I suspect that for most of them the
reason is more that they like working than that they want the
money.

Income Effects in Production and the
Backward-Bending Supply Curve for Labor

The mistake in the analysis that produced Figure
5-1a is the omission of what was described in Chapter 3 as the income
effect. An increase in wages (say, from $10/hour to $11/hour) has two
effects. It makes leisure more costly--each hour not worked means $11
less income instead of $10. That is an argument for working more
hours at the higher salary. But at the same time, the increased wage
means that the producer is wealthier--and is therefore inclined to
consume more leisure. It is possible for the second effect to
outweigh the first, in which case the increased wage causes a
decrease in hours worked, as shown in Figure 5-4. This is called a
backward-bending
supply curve for labor; the backward-bending portion is from F to G
(and presumably above G). The result, in the case of a single
producer, would be a supply curve for goods that sloped in the wrong
direction; for some range of goods, higher prices would generate less
output instead of more.

This is not the first time we have seen a conflict
between income and substitution effects. In Chapter 3, the same
situation generated a Giffen good--a good whose demand curve sloped
in the wrong direction. I argued that there were good reasons not to
expect to observe Giffen goods in real life. Those reasons do not
apply to the backward-bending supply curve for labor.

One of the reasons was that while we expect
consumption of most goods to go up when income goes up, a Giffen good
must be a good whose consumption goes down with increasing income--an
inferior good. Indeed, it must be so strongly inferior that the
income effect of an increase in its price (which, since we are buying
it, is equivalent to a decrease in real income) outweighs the
substitution effect. Our labor is something we are selling, not
buying; an increase in its price (the wage rate) makes us richer not
poorer, and so inclined to buy more leisure. So the backward-bending
supply curve for labor only requires leisure to be a normal
good.

The other reason a Giffen good is unlikely is that
it must be a good on which we spend a large fraction of our income,
in order that the decrease in its price can have a substantial effect
on real income. This is implausible in the case of consumption, but
not in the case of production. Most of us diversify in consumption
but specialize in production; we divide our income among many
consumption goods, but we get most of that income from selling one
kind of labor. If the price we get for what we sell changes
substantially, the result is a substantial change in our income.
Hence the backward-bending supply curve for labor is far more likely
to occur than is the Giffen good.

A backward-bending supply curve for
labor. As the wage increases, the number
of hours worked first increases (up to point F), then decreases.

Economics is considerably simpler if demand curves
always slope down and supply curves always slope up than if they
insist on wriggling about as in Figure 5-4. Fortunately the argument
for upward-sloping supply curves for goods does not entirely depend
on upward-sloping supply curves for labor. If individuals supply less
labor, and so mow fewer lawns, as the price of lawn mowing rises,
their individual supply curves will slope backward. But if an
increase in the price increases the number of people who find that
lawn mowing yields a higher wage than any other alternative, the
aggregate supply curve for lawns may still slope normally. It is
particularly likely to do so in a large and complicated society. If
many different goods are being produced, with the production of each
employing only a small part of the population, even a small rise in
the price of a good can induce some people to switch to producing it.
It is still more likely if, as seems likely, only some of the
producers are on the backward-bending portion of their supply curve
for labor.

Marginal Value vs Marginal Utility

Another way of looking at the problem of the
backward-bending supply curve for labor is as a result of the effect
of a change in income on the relation between marginal value and
marginal utility. When your wage increases from $10/hour to $11, you
are being offered more dollars for your time than before, but since
at the higher income each dollar is worth less to you (the marginal
utility of income has fallen), you may actually be being offered less
utility--$11 at your new, higher income may be worth less to you than
$10 was before. If so, and if the marginal utility of leisure to you
has not been changed by the increase in your income, you will choose
to sell less of your time at the higher wage, and so work fewer
hours. If the marginal utility of leisure has increased (you now have
more money to spend on golf games and Caribbean vacations), the
argument holds still more strongly.

The analysis of production given in the first part
of this chapter (ignoring income effects) would correctly describe a
producer whose income from other sources was large in comparison to
his income from production. Changes in his wage would have only a
small effect on his income, so we could legitimately ignore the
income effect and consider only the substitution effect. The result
would be the sort of curves shown in Figures 5-1a, 5-1b, and 5-2. It
would also correctly describe a producer facing only a temporary
change in his wage. He can transfer money from one year to another by
saving or borrowing, so the value of money to him depends not on his
current income but on some sort of lifetime average--his
permanent income. His permanent income is changed only very slightly by
changes in this week's wage, so the income effect of a temporary wage
change is small.

The question of whether the supply curve for labor
was or was not backward bending was a matter of considerable
controversy 200 years ago, when Adam Smith wrote The Wealth of Nations, the book
that founded modern economics. Some employers argued that if wages
rose their employees would work fewer hours and the national income
would fall; Smith argued that higher wages would mean better fed,
healthier employees willing and able to work more in exchange for the
higher reward. It is worth noting that Smith, who is usually
described as a defender of capitalism, consistently argued that what
was good for the workers was good for England and almost as
consistently that what was good for the merchants and manufacturers
(high tariffs and other special favors from government) was bad for
England. He was a defender of capitalism--but not of
capitalists.

PART 3 --INDIFFERENCE CURVES AND THE
SUPPLY OF LABOR

So far, we have analyzed the supply curve for
labor, or for goods or services produced by labor, by using marginal
value curves. Another way is by using indifference curves. The
indifference curves on Figure 5-5 show an individual's preferences
between leisure (defined, at this point, as any use of your time that
does not bring in money) and income. Using such a diagram, we can
derive a supply curve for labor in a way that allows for the
possibility that it may be backward bending. Figure 5-5a shows the
production possibility sets (possible combinations of leisure and
income) corresponding to wages of $5, $10, and $15/hour, along with
the corresponding indifference curves and optimal bundles, for an
individual with no other source of income. In each case, one
possibility is 24 hours per day of leisure and no income. Another is
no leisure and a daily income of 24 times the hourly wage. With a
wage of $5/hour, for example, the line runs from 24 hours of leisure
and no income to no leisure and an income of $120/day. The available
combinations of leisure and income on Figure 5-5a correspond to
points on the line between those two extremes. As the wage moves from
$5 to $10 to $15/hour, the line moves from W1 to W2 to W3 and the optimal bundle from
A1 to
A2 to
A3 .

Indifference curve/budget line diagrams for
calculating the supply curve of labor. The
budget lines show the alternative bundles of leisure and income
available to a worker at different wage levels; the indifference
curves show his preferences among such bundles. The indifference
curves of Figure 5-5a lead to a normaly sloped supply curve for
labor; those of Figure 5-5b lead to a backward-bending supply curve
for labor.

The indifference curves illustrated in Figure 5-5a
imply a normal supply curve for labor, at least over the range of
wages illustrated; as the wage rises, so does the number of hours
worked (shown by a fall in the number of hours of leisure). Figure
5-5b illustrates a different set of indifference curves, leading to a
backward-sloped supply curve. Figure 5-6 shows the two supply curves,
S1 (obtained
from Figure 5-5a) and S2 (from Figure 5-5b).

Students who try to redo the calculations shown on
Figures 5-5a, 5-5b, and 5-6 in homework (or exam) problems frequently
make the mistake of assuming that they can simply connect points such
as A1 ,
A2 , and
A3 with a
line, and then redraw the same line on another graph as the supply
curve for labor. But the vertical axis of Figures 5-5a and 5-5b is
income, while the vertical axis of Figure 5-6 is the wage rate;
income is wage (dollars/hour) times number of hours worked. The wage
on Figure 5-5a is not the height of a point but the slope of a line.
W1, for
example, has a slope of (minus) $5/hour and shows the alternatives
available to someone who can work at that wage. The point on Figure
5-6 that corresponds to A1 on Figure 5-5a is
C1; its
vertical coordinate is $5/hour (corresponding to the slope of
W1) and its
horizontal coordinate is 7 hours per day (corresponding to the number
of hours worked at A1--24 hours per day total minus 17 hours per day of
leisure). You may want to check for yourself the correspondence
between A2
and C2 and
between A3
and C3.

You may have realized by this point that what we
are analyzing in this chapter is simply a special case of what we
already analyzed in Chapters 3 and 4. Instead of talking about a
supply of labor and a marginal disvalue for labor, we could have
started with an individual who had an endowment of a good called
leisure (24 hours per day), which he could sell at a price (his wage)
and for which he had a marginal value curve. Just as in Chapter 4,
the marginal value curve is identical to the demand curve. The
marginal value for leisure curve is the same as the marginal disvalue
for labor curve, and the demand curve for leisure is the same as the
supply curve for labor, except that in each case the direction of the
horizontal axis is reversed--increasing leisure corresponds to
decreasing labor.

Our old friend the equimarginal principle applies
here as well. The individual sells an amount of leisure (works a
number of hours) such that the value of a little more leisure (the
disvalue of a little more labor) is just equal to the price he is
paid for it. In equilibrium, the wage equals the marginal value of
leisure (marginal disvalue of labor).

The supply curves for labor implied by Figures
5-5a and 5-5b. Points C1, C2, and C3 correspond to points
A1,
A2, and
A3 on Figure
5-5a. Note that the vertical axis of this figure shows wage, not
income; wage on Figures 5-5a and 5-5b is not the height of a point
but the slope of a line.

OPTIONAL SECTION

PRODUCTION--MORE COMPLICATED CASES

So far, we have considered production under
relatively simple circumstances. Producers sell their output on the
market, so all they have to know in order to decide what to produce
is how much it sells for. Amount of production, for any good, is
simply proportional to amount of time spent producing it. In this
section, we will consider some more complicated cases.

Production without a Market

So far in my discussion of production, I have
assumed that the producer sells his output rather than consuming it
himself. Figure 5-7 shows one way of analyzing the alternative--a
situation where you consume your own output. MV is the marginal value
to you of mowed lawns; MdV is the marginal disvalue of your labor.
Your rate of output is 1 lawn per hour. The horizontal axis shows how
many mowed lawns you produce and consume. You consume a mowed lawn by
enjoying the view--I am not assuming that you eat grass.

Marginal value/marginal cost diagram for a
producer who consumes his output himself. On Figure 5-7, the marginal cost of production is the
marginal disvalue of labor; since the output rate is one lawn per
hour, the vertical axis can be read as either dollars per hour or
dollars per lawn, and the horizontal axis can be read as either lawns
per day or hours per day.

If the quantity is less than Qe , where the two curves
cross, then the marginal value of the good is greater than the
marginal disvalue of the labor used to produce it. That means that if
you produced an additional unit, the value to you of the good would
be more than the cost to you of the labor used to produce it, so you
would be better off producing it. That remains true as long as
quantity is less than Qe, so you keep increasing your
level of output (and consumption) until it reaches Qe. Beyond that, additional
units cost you more labor than they are worth, so any further
increase in output would make you worse off.

Figure 5-7 shows a situation where only one kind
of good can be produced. Figure 5-8 shows a situation where two goods
can be produced--meals and mowed lawns. The individual's preferences
between them are shown by indifference curves, as in Chapter 3. If he
chooses to work 10 hours per day, he can produce 10 lawns, or 20
meals, or any intermediate bundle; his production possibility set is
the colored area on Figure 5-8. The optimal bundle is the point in
the set that intersects the highest indifference curve--point A on
the figure. The diagram is exactly the same as for an individual with
an income of $10/day who is able to buy lawn mowing at $1/lawn and
meals at $0.50/meal. In each case, the individual chooses the best
bundle from a collection that includes ten lawns (and no meals), 20
meals (and no lawns), and everything in between.

If you move back from the picture, however, and
think about what it means, there is one important difference between
the two cases. In discussing a consumer spending money, I argued that
he would always spend his entire income, since the only thing money
is good for is buying goods. The equivalent in the case of time is
always working 14 hours per day--or perhaps 24!

The problem is that in drawing Figure 5-8, I
implicitly assumed that the only things that matter to you are meals
and mowed lawns--in particular, I assumed that you have no value at
all for your own leisure. If that were true, you would work 24 hours per day. In
drawing the figure, I have correctly translated the assumption into
geometry without pointing out, until now, that the assumption itself
is absurd. That is an example of why it is a good idea to move back
and forth between mathematical and verbal descriptions, in order to
make sure you know what your mathematics actually stands for. It is
not unusual for articles to be submitted to economics journals that,
when translated into English, turn out to make no sense. Some of them
get published.

What the figure can be used for is to show what
combination of the two goods the individual will choose to produce
if he decides to
work a certain number of hours. To find out how many hours he would
choose to work, we would need to add a third dimension in order to
show his preferences among meals, lawns, and leisure.

Indifference curves and production possibility
set for an individual working 10 hours per day. The individual can produce 10 lawns per day or 20 meals
per day; different points on the line between 10 lawns and 20 meals
represent different divisions of time between producing lawns and
producing meals. A is his optimal point.

Nonlinear Production

Let us now drop another assumption. So far, the
output of each good has been proportional to the time spent producing
it. As a result, the frontier of the production possibility set for
any pair of goods (total hours worked held constant, as in Figure
5-8) is a straight line, like a budget line. The similarity is not
accidental. In Chapter 3, the consumer got goods by spending money;
in this chapter, he gets them by spending time. In both cases, total
expenditure is simply the sum of the price of one good--in money or
in time--multiplied by the quantity of that good bought plus the
price of the other good multiplied by the quantity of it
bought.

Figure 5-9a shows a more complicated case--the
production possibility set of someone who is more productive if he
specializes. If he spends all his time mowing lawns, he can maintain
his lawn-mowing skills at a high level and mow more lawns per hour
than if he spends much of his time cooking. If he spends all his time
cooking, he can maintain his culinary skills at a high level and
produce far more meals per hour than if he spends most of his time
mowing lawns. (Perhaps our measure of quantity of meals cooked should
include some allowance for quality as well, so that a meal cooked by
a professional mower of lawns is equivalent to 1/10 of a meal cooked
by a Cordon Bleu chef). Point J shows what happens if he tries to
divide his time between lawn mowing and cooking, making himself "a
jack of all trades and a master of none."

Figure 5-9b shows a production possibility set
whose boundary curves in the opposite way. You may think of this as
describing someone who could engage in two quite different kinds of
production--digging ditches and writing sonnets. Digging ditches uses
the producer's muscles; writing sonnets uses his mind. He can compose
a few more sonnets per day if his mind is not distracted by ditch
digging, and he can dig a few more ditches if he is not trying to
find three more words that rhyme with "world" for the octave of a
Petrarchan sonnet. But the two activities compete with each other
only mildly, producing the curve shown in the figure.

Two cases of non-linear production.
The individual is producing goods to sell.
The shaded areas are the different bundles that he can produce. The
straight lines are equi=income curves; each shows all the different
bundles that sell for a given amount of money. The producer wants to
produce the bundle that sells for the largest amount. That will be
the point in the shaded region that touches the highest equi-income
curve.

Let us now go back to the problem with which we
started this chapter--which good to produce. As in the earlier
discussion, we assume the individual is producing goods to sell on
the market rather than for his own consumption. We can reproduce the
argument of Table 5-1, in this more complicated situation, by adding
to our figure equi-income
lines--lines that show the different
bundles of goods that can be sold for the same total amount. These
are indifference curves from the standpoint of the producer, since
all that matters to him about his output is what he can sell it for.
Unlike our usual indifference curves, these are straight lines. If
lawn mowing sells for $10/lawn and meal cooking for $5/meal then if
you start with a bundle of 10 lawns and want to construct other
bundles that will bring you the same amount of money ($100), you find
that each time you subtract 1 lawn you must add 2 meals. The result
is a straight line, as shown on Figures 5-9a and 5-9b. The slope of
the line depends on the relative prices of the two goods. Picking the
optimal set of goods to produce is easy. For any number of hours you
consider working, find the highest line that touches the
corresponding production possibility set; the point where they touch
is the most valuable bundle you can produce with that amount of
labor.

By looking at Figure 5-9a, you should be able to
convince yourself that whatever the slope of the equi-income lines,
the highest equi-income line that touches the production possibility
set touches either at one end of the curve (all lawns) or at the
other (all meals) or possibly at both, but never anywhere in the
middle. This corresponds to what we usually observe--people
specialize in production, spending all their time (aside from home
production--cooking your own food and washing your own face)
producing a single good or service. The situation of Figure 5-9b, on
the other hand, while it can lead to specialization (if the slope of
the line is either very steep or very shallow, implying that one of
the goods has a very high price compared to the other), can also lead
to diversified production, as in the case shown.

Figures 5-9a and 5-9b look very much like
indifference curve diagrams, especially Figure 5-9a. In a way they
are, but the straight line and the curve have switched roles. In an
ordinary indifference curve diagram, the straight line is a budget
line, showing what bundles of goods the consumer can choose among.
The curve is an indifference curve, showing what bundles are equally
attractive to him. On Figure 5-9, the curves are the equivalents of
budget lines--they show the different bundles of goods the consumer
can choose to produce. The straight line equi-income curves are
indifference curves--since the goods are being produced for sale, the
producer is indifferent between any two bundles that sell for the
same amount.

From another standpoint, the straight line
equi-income curve of Figure 5-9 and the straight budget line of
Chapter 3 are the same line. Both show all bundles of goods that cost
a given amount of money. From the standpoint of the consumer with a
certain amount of money to spend, the line represents alternative
bundles that he can buy with that amount of money. From the
standpoint of the producer, it represents alternative bundles that he
can sell to get that amount of money. It is the same transaction seen
from opposite sides.

The logic of what we are doing here is essentially
the same as in Chapter 3. An individual has objectives (utility from
consumption for the consumer, utility from income and leisure for the
producer) and opportunities. He chooses that one of the available
opportunities that best achieves his objectives. The geometric
apparatus of budget lines and indifference curves is simply one way
of formalizing the definition of economics at the beginning of
Chapter 1, one way of analyzing people who have objectives and tend
to choose the correct way to achieve them.

PROBLEMS

2. Figure 5-10a shows your marginal disvalue for
labor curve. You can make $8/hour washing cars or $6/hour waiting on
tables. What is your producer surplus from washing cars? In other
words, how much worse off would you be if the carwash closed
down?

3. Your rich uncle just died and left you, to your
surprise, a $10,000/year trust fund. Figure 5-10a used to describe
your supply curve for labor. What do you think your labor supply
curve might look like now? Draw it.

4. You can produce 3 falchions/hour or 5
petards/hour. Figure 5-10b shows your supply curve for labor. Draw
your supply curve for falchions, assuming that the price of a petard
is $2. Draw your supply curve for petards, assuming that the price of
a falchion is $4 .

5. Some people, such as scoutmasters and PTA
officials, are willing to work at jobs that pay nothing--even, in
some cases, at jobs that pay less than nothing. Draw a labor supply
curve for such a person.

6. In the text, I prove that the producer surplus
calculated from the summed supply curve for two producers is the sum
of the producer surpluses calculated separately. Prove the same
result for consumer surplus.

7. Prove the same result for three
producers.

8. Prove that the result applies to any number of
producers.

9. In the examples discussed, producer surplus is
always less than salary. Can you think of a situation where it would
be greater? Discuss.

10. "At a cost of only $10,000,000 a year of
public expenditure, this administration, by attracting new firms into
the state, has increased the income of our citizens by $20,000,000.
The citizens should be grateful; for every dollar of tax money they
give us, we are providing them $2 of income." Assume the facts are
correct; discuss the conclusion in terms of the ideas of this
chapter.

11. The production possibility lines on Figure 5-5
were drawn on the assumption that if you spend no hours working you
have no income. Draw a budget line for someone who receives $10/day
from his parents and, in addition, can work as many hours as he
wishes for $5/hour.

12. What are some other situations that the budget
line you drew for the previous question might describe?

13. Draw a budget line for someone who can work as
many hours as he wishes for $10/hour, but must pay $20/day interest
on his accumulated debts.

14. What are some other other situations that the
budget line you drew for the previous question might also
describe?

15. In Chapter 4, I rejected the idea that
economists assume individuals value only income. Draw a set of
labor/leisure indifference curve for someone who always prefers more
income to less, whatever the cost in other values. How many hours a
day will he work?

16. Figure 5-11 is an indifference map showing
your tastes for leisure and income. Draw the corresponding supply
curve for labor over a range of wages from $1-$10/hour. How does it
slope? Show how you calculated it.

Indifference curves showing preferences with
regard to income and leisure. For Problem
16

The following problems refer to the optional
section:

17. In the situation shown in Figure 5-7, how much
worse off would you be if you were forbidden to produce anything?
Discuss your answer in terms of producer surplus and consumer
surplus.

18. Use indifference curves to explain why we
usually do not specialize in consumption. Use indifference curves to
show a situation where an individual does specialize in consumption.
This particular kind of solution to the decision problem illustrated
on an indifference curve diagram has a name; what is it?

19. Draw an indifference curve diagram showing the
producer of Figure 5-9a producing goods for his own consumption.
Where is his optimal point? Is he specializing or
diversifying?

20. Draw an indifference curve diagram showing the
producer of Figure 5-9b producing goods for his own consumption.
Where is his optimal point? Is he specializing or diversifying?